Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

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We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.
21 pages, To appear in Compositio Mathematica

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Classical Analysis and ODEs, Number Theory, 33E20 (Primary) 33C05, 11G55 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/130516

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310061
 http://arxiv.org/abs/math/0310061
 Compositio Mathematica, Vol. 139, Issue 1, October 2003, pp. 85--100. MR2024966 (2005f:11196)
 doi:10.1023/B:COMP.0000005036.52387.da

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